Answer : The value of
is 286.2 J and 286.2 J respectively.
Explanation : Given,
Moles of sample = 0.877 mol
Change in temperature = 15.7 K
First we have to calculate the heat absorbed by the system.
Formula used :
![q=n\times c_v\times \Delta T](https://tex.z-dn.net/?f=q%3Dn%5Ctimes%20c_v%5Ctimes%20%5CDelta%20T)
where,
q = heat absorbed by the system = ?
n = moles of sample = 0.877 mol
= Change in temperature = 15.7 K
= heat capacity at constant volume of
(diatomic molecule) = ![\frac{5}{2}R](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7DR)
R = gas constant = 8.314 J/mol.K
Now put all the given value in the above formula, we get:
![q=0.877mol\times \frac{5}{2}\times 8.314J/mol.K\times 15.7K](https://tex.z-dn.net/?f=q%3D0.877mol%3C%2Fp%3E%3Cp%3E%5Ctimes%20%5Cfrac%7B5%7D%7B2%7D%5Ctimes%208.314J%2Fmol.K%5Ctimes%2015.7K)
![q=286.2J](https://tex.z-dn.net/?f=q%3D286.2J)
Now we have to calculate the change in internal energy of the system.
![\Delta U=q+w](https://tex.z-dn.net/?f=%5CDelta%20U%3Dq%2Bw)
As we know that, work done is zero at constant volume. So,
![\Delta U=q=286.2J](https://tex.z-dn.net/?f=%5CDelta%20U%3Dq%3D286.2J)
Therefore, the value of
is 286.2 J and 286.2 J respectively.